Nonsingularity of the direct scattering transform for the KP-2 equation with real exponentially decaying at infinity potential

摘要

We study the direct spectral transform for the heat equation, associated withthe KP-2 equation. We show, that for real nonsingular exponentially decaying atinfinity potentials the direct problem is nonsingular for arbitrary largepotentials. Earlier this statement was proved only for potentials, satisfyingthe ``small norm'' assumption.